2009 Concordia Math May Seminar
 2009 Student Photo Journal
 I now see math in a completely different light than before. I used to think of math as a way to figure out abstract problems. Now, I see math as a way to improve our lives and make our world easier. I see math as a subject with great dynamic history and a participant in numerous important events and projects. Most of all, I now see math as a field with a lot of potential and many discoveries needing to be found.
 When I first heard about the math department's May Seminar to Egypt and Europe, I knew that it would be a onceinalifetime experience for me. I also knew that I would have a tough time convincing my parents to let me go. I didn't really understand the connection between the places we were going and the history of mathematics. After much persuasion I finally convinced them that going on this trip would benefit my mathematical education, even though at the time I couldn't see how it could.
After we finally started the nightly classes, I finally saw the historical aspect of math a whole lot clearer. I began to realize that the concepts of geometry, algebra, calculus, and other fields of math weren't found in a treasure chest somewhere. They had to be discovered and sculpted by many brilliant people over the course of thousands of years. Moreover, those concepts weren't created to make math tests harder, but rather to come up with ways to solve difficult, practical problems.
 "Mathematics is the language of life." Before this trip, I had always believed that statement, but this May Seminar gave me a chance in a whole new way to see how true that statement really is. By learning about the history of mathematics, its connection with other arts & sciences, and travelling to actual historical sites, I was able to see mathematics in another light in a way that will stay with me for the rest of my life.
 When I started taking math classes at Concordia, I developed an interest in finding out the origins of mathematical concepts. I studied proofs, theorems, and the reason for their discoveries. I began to see mathematics not just as a series of equations and formulas, but as a powerful entity with a rich history and a world of discoveries yet to be made. Acquiring this new perspective made me all the more eager to learn all the concepts of math and to contribute positively to the field.When I started taking math classes at Concordia, I developed an interest in finding out the origins of mathematical concepts. I studied proofs, theorems, and the reason for their discoveries. I began to see mathematics not just as a series of equations and formulas, but as a powerful entity with a rich history and a world of discoveries yet to be made. Acquiring this new perspective made me all the more eager to learn all the concepts of math and to contribute positively to the field.
 Another thing this trip showed me was how mathematics relates to art and science and how it can be found everywhere you look. At the Tower of London, we learned that a mathematician used polyhedral to invent a new, more brilliant diamond cut for the crown jewels. The mathematician Pozzo painted the Sant' Ignazio ceiling in Rome and used linear perspective to give a 3D effect. That painted dome was something you could not just learn about in a classroom. You had to see it for yourself in person in Italy to experience the full effect and to fully understand it. All of the artwork that we saw reminded me of the Pi Mu Epsilon Conference talk on Caravaggio in which the student speaker used mathematics to analyze what made a good painting.
 I knew before that the Greeks developed proofs, but I never realized how advanced their proof techniques were. A good proportion of the things we learned about in Modern Algebra last semester (at least the number theory stuff), the Greeks already knew and had proven over 2000 years ago! That is absolutely mindblowing to me. However, by far, my favorite mathematicalrelated artifact we saw on this trip was the Antikythera Mechanism, the first analog computer. To actually see it in person & to see the teeth on the gears was amazing to me. It was fascinating to see the reconstruction with all of its gears and realize how complicated of a mechanism it actually was.
 I got a big idea of how art and math can be connected when I visited the Salvador Dali exhibit in Paris. You would never imagine that Dali, a famous surrealistic artist, could use science as inspiration. However, it seems Dali's later art was inspired by current discoveries in the field of physics and science. Crucifixion (Corpus Hypercubus), which depicts Christ on a cubic cross, was a recreation of a picture he saw of the crystallization of salt in space. The Disintegration of the Persistence of Memory, a sequel to his most famous painting, applied the concepts of nuclear physics and genetics. Dali's Christ of St. John of the Cross was inspired by a dream he had about geometrical shapes. Even The Sacrament of the Last Supper features a dodecahedron to represent the twelve disciples. To Dali, he considered the concepts of math and science as a part of nature and religion, and therefore a part of art.
 Hiking in the Alps reminded me that all mathematicians need to take time out to be revitalized and inspired. Cantor and Dedekind used to go hiking in the Alps and I can see why. The Alps are something that needs to be experienced, not simple seen in pictures. It was easy to draw inspiration from the beautiful scenery around us. That is a lesson I will take with me leaving this trip.
 I am so glad I was able to come on this May Seminar and so grateful for the incredible opportunity that it was. I would go again in a heartbeat. I learned a lot and the chance to actually visit the places we learned about was absolutely unbelievable. Throughout the semester and the past month, my understanding and experience of mathematics has broadened as I have learned about its history and how it relates to the world around me. The lessons I've learned and the experiences I've had are something I will keep with me for the rest of my life.
 I have learned that many seemingly unrelated aspects of history and culture can be studied through a "mathematical lens". Today, our idea of "math" is much more complicated than it once was. An appreciation of seemingly simple math (proportions, geometry, counting) makes the study of history and societal development very fascinating. As a future math teacher, I can use some of these interesting sites and cultures to engage my uninterested students in math!
 This past semester and especially this past month have greatly changed the way that I view mathematics. I truly have come to view mathematics in another light. I have seen how mathematics can advance arts, sciences, cultures, and civilizations. It is one thing to sit in classrooms at Concordia and learn about calculus and proofs and other mathematical concepts, but the experiences I have had this May have given a real context to everything I have learned in the classroom.
 One thing that taking this May Seminar has done for me is help me learn about other Concordia math students. I really enjoyed getting to know other math majors who are older than me and therefore classes ahead of me. Getting to talk to them about their experiences and ambitions has been a huge part of my experience and has caused me to see mathespecially math at Concordiain a new light. It has caused me to take another look at which classes I might want to take, and more importantly it has caused me to stop and think about what I want to do after Concordia. Meeting the other students on this trip has been a very positive component of the experience.
 Just as Egypt showed me the importance of math in architecture and engineering, Italy showed me how important mathematical perspective has been to art since the time of the Renaissance. It was really neat to walk into Italian churches and look up at the ceiling and see for myself the obvious use of mathematical perspective and vanishing points. I really noticed it in museums like the Uffizi where there were plenty of paintings that were `flat` and had been done before the advent of perspective mixed in with those that had obviously been done with a lot of attention to linear perspective. Comparing the before and after there really illustrated how important math has been to art in the last 500 years. It really showed me that math truly is everywhere and really is important in almost any field. It was a great illustration of the universality of mathematics. I can't wait to see how these new perspectives will enrich the rest of my math education at Concordia and beyond.
 Throughout this trip I learned a lot about how math is used and where it shows up in places other than in the classroom. I was able to see how architecture and engineering used math to create great things like the pyramids and Stonehenge. It also showed me how structures have evolved along with the evolution of math. I also found it quite exciting to see math show up in art through perspective and theater through the golden ratio. It was wonderful to see how many different ways math can be used and I hope to show of these ways to my students once I become a math teacher.
 Being a part of this class definitely opened my eyes to a whole new world of possible applications I had either forgotten about, or simply never considered. It was fun to have a class that talked a lot about realworld applications from ancient times because it made it clear how important math has been throughout the history of the world. It has also made it easier to see how math has progressed over the years. This has truly been the trip of a lifetime because it not only opened my eyes to places and ways math is used that I hadn't previously considered, but it also gave me numerous ideas for applications that will interest my future students.
 Honestly, the original reason I signed up for this class was not for any academic reasons. I did not expect to learn much about math. I just wanted to see all of the cool places. On this 25day excursion, I not only saw all of the places I wanted to see, but I learned much more about math than I could possibly imagine. I learned about the history of math, applying math to other subjects, and math in everyday life. I liked that I learned something different about math in every country we visited.
